Internal Rate of Return IRR and Linear Interpolation - Engineering Economics Lightboard

[@loltwest9423]

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[@EngineeringEconomicsGuy]

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[@EngineeringEconomicsGuy]

Troy, you can email me at [e-mail] if you like! Glad you like my videos!

[@yaimelcastro7838]

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[@EngineeringEconomicsGuy]

Glad you like the channel. Thanks for the comment!

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[@EngineeringEconomicsGuy]

Happy to help! Good luck.

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[@EngineeringEconomicsGuy]

You're welcome!

[@TheCamillejr]

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[@norencezyron.bedasua]

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[@EngineeringEconomicsGuy]

Glad it helped!

[@BlitzHitz]

Engineering Economics Guy, thank you.

[@EngineeringEconomicsGuy]

You're welcome!

[@d.b2370]

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[@EngineeringEconomicsGuy]

Happy to help! Good luck in your course!

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[@EngineeringEconomicsGuy]

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[@AsalAsal-fv7px]

I'm a little confused about something and hope you can clarify. When calculating the IRR using the interpolation method, it is easy when there is only one factor in the equation, but what if there is more than one factor. For example: 50,000 = 15,000 (P/A; i*;5) + 16,384 (P/F; i*;5). Here, there are 2 factors (P/A) and (P/F). Which tables should I look at to interpolate, or in these cases, must I use trial and error?

[@EngineeringEconomicsGuy]

Excellent question! Yes, the kind of simple interpolation demonstrated in this video is not possible when there are multiple terms in the equation. You are correct - you need to use trial-and-error, or perhaps a numerical method to solve for i.

[@AsalAsal-fv7px]

@@EngineeringEconomicsGuy Awesome. Thank you so much! I really appreciate you getting back to me.

[@EngineeringEconomicsGuy]

No problem! Good luck in your course!

[@erwandomine6563]

dumb question, but how are you writing on glass in the right way so the assistance doesn't have it inverted?

[@EngineeringEconomicsGuy]

The video is mirrored using software. Good question!

[@AsalAsal-fv7px]

Thank you so much for this explanation. I have a question about a couple of examples in the book and how the IRR was calculated. The first one used (P/F;i*,N), and the answer was right away the IRR. The second example used (A/P;i*,N), but the i calculated was used to interpolate to get the IRR. My question is: why, when using the P/F , do we get the IRR, but when using the A/P we do interpolation to get the IRR. I hope this makes sense without me being able to copy and paste the answers.

[@EngineeringEconomicsGuy]

This is an excellent question. I think the answer you're looking for relates to the 'math' involved in solving for the value of IRR. In problems with a P/F compound interest factor (or an F/P), it is possible to solve the equation 'explicitly' for the unknown variable "i"; meaning, you can rearrange the equation and isolate the "i". This leads to an immediate and exact solution. On the other hand, for problems involving A/P (or P/A), the equation CANNOT be explicitly solved for "i"...no matter how good you are at algebra - it just doesn't work. Have a look at the formula for A/P and you'll see what I mean. For problems like this it is necessary to use one of the following methods to solve for "i": linear interpolation, trial-and-error, numerical techniques, or the built-in 'solver' or 'goal seek' functions in Excel. Excel also has an "IRR" function that does the job for you. I have a video on using Excel for this purpose! kzbin.info/www/bejne/hJSyaH-vf6prmKM It's a little complicated, but I hope this answer is helpful! Good luck in your course!

[@AsalAsal-fv7px]

@@EngineeringEconomicsGuy Thank you so much. It makes so much sense. I really appreciate your help!

[@EngineeringEconomicsGuy]

My pleasure! All the best!

[@rcaone]

Thank you a lot. If we have mutliple cash flow....I think this will be hard to solve this way....using the NPV formula ( IRR = unkown i ) and finding the IRR which bring the NPV to 0. Is this the correct way ?

[@EngineeringEconomicsGuy]

Yes. What you've said is correct. Also, using linear interpolation can be slow and tedious. Excel has a built-in function called "IRR"- this is by far the easiest way to solve these problems! Although, understanding linear interpolation can be useful for engineering students in other courses, and it does help students understand numerical methods for solving problems, even though this is very basic.

[@engineeringlecturesandexpe3091]

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[@EngineeringEconomicsGuy]

Thank you so much!

[@deadman4167]

A big help, thank you!

[@EngineeringEconomicsGuy]

Glad it helped!

[@nauman8030]

How to find i* if we also have a salvage value? I mean if there is a salvage value its not easy to get i*(for example i*=5 in the question)?

[@EngineeringEconomicsGuy]

Excellent question! The time-value-of-money equation is not so simple to interpret if there is a salvage value. The only option is to find the solution using a 'numerical method'. The best option is to use the 'goal seek' function or the 'solver' in MS Excel. Of course the other option is simple "trial-and-error"! I hope this answers your question.

[@shaveenh.husien]

Why I Can't find the Break- even analysis and Cost-Benefit Analysis Methods ?!

[@EngineeringEconomicsGuy]

Perhaps my video called 'Payback Period' is closer to the type of analysis you're looking for: kzbin.info/www/bejne/hIqZq2WqjL2ki8U Hope this helps!

[@wongcaleb1157]

How do we solve such question if the cashflow are different throughout the years?

[@EngineeringEconomicsGuy]

Solving for an unknown interest rate when the cashflows are irregular is difficult! In these cases, you can still write the 'time-value-of-money' "equation" but it will have several terms that include the unknown value of 'i'. Solving the equation for 'i' will require the use of a numerical-method (a fancy way of saying "let a computer perform some clever type of 'trial-and-error'"). MS Excel has a 'Goal Seek' function that I use for problems like this. -Good Question!

[@wongcaleb1157]

@@EngineeringEconomicsGuy thanks for your efficient response and explaination. No doubt u are a lifesaver like everybody says..

[@EngineeringEconomicsGuy]

You're welcome! And thanks for the nice comment!!

[@shaveenh.husien]

Why we didn’t use the equation of discount factor?

[@EngineeringEconomicsGuy]

Unfortunately, you can't solve the equation 'explicitly' - meaning you can't isolate the value of "i" using algebra. Trial-and-Error or Linear Interpolation are simple suggestions for solving for the value of "i". However, the best method is to use a numerical solver in a calculator or in a program like Excel. In fact, Excel has a built-in function called "IRR" that will solve problems like this automatically. Watch my video: kzbin.info/www/bejne/hJSyaH-vf6prmKM for the best way to solve these problems.

[@ainasabrina3148]

Hi sir, I would like to ask. 1. Does the meaning of the market value of 100 dollars after five years of usage is the same with the returns value of 100 dollars at the end of the year? 2. Also, what is the meaning of, 'the estimated increased productivity attributable to the new equipment is amounting a total of 500 dollars per annum after extra operating costs have been subtracted from the revenue generated by the additional production'? Earlier, I was assuming the market value as the salvage value and the estimated increased as the annuity. thank you in advance because I had a confusion regarding my tutorial question just now.

[@EngineeringEconomicsGuy]

OK - So I think your questions are not about this video, BUT that's OK! For your question (1), I think the answer is yes. For your question (2), you are correct that the 'estimated increase' is the annuity, and the market value is the same as the salvage value. I hope this helps - although it seems you already had the correct assumptions. Engineering Economics is often more about understanding WORDS than it is about understanding NUMBERS!!

[@ainasabrina3148]

@@EngineeringEconomicsGuy yes sir, because I have gone through most of the related topic of your videos, so I just simply comment here what I don't understand. I think I could figure out the solution. Thank you for the fast reply sir! May God bless you..

[@EngineeringEconomicsGuy]

Ok, I'm happy to help. Good luck in your course!

[@AhmedSajawal]

life saver

[@EngineeringEconomicsGuy]

Glad I could help! Good luck to you!

[@AhmedSajawal]

@@EngineeringEconomicsGuy Thank you sir ❤️

[@shivamnahata7451]

i know how to do interpolation annuity i am confused in that like 28.5714 is the difference between 14and 15% I am confusing still.

[@EngineeringEconomicsGuy]

I'd like to help you but perhaps your question does not relate to this video? In this video the interpolation occurs between 5% and 6% for values of the P/A compound interest factor of 5.0756 and 4.9172. I don't see where your values of 28.5714 or 14% and 15% are coming from? Perhaps you can clarify your question?

[@shivamnahata7451]

@@EngineeringEconomicsGuy I just give an example sir.

[@EngineeringEconomicsGuy]

From the example in this video, we know that the value of the (P/A compound interest factor) must equal 5.000 BUT we don't know what value of 'i' makes this true. The P/A compound interest factor is a complicated formula that cannot be 'solved' for 'i' using algebra, SO, we approximate a value by linear interpolation between the value of 5.0756 (for i=5%) and 4.9172 (for i=6%). 5.000 is "part-way" between 4.9172 and 5.0756 - if we find out exactly 'how much between' we can use this same 'amount-between' to find an answer 'between' 5% and 6%. I think maybe you need to know more about what the P/A compound interest factor is before you can fully understand this example. I suggest you explore my playlist on 'Cash Flow Analysis': kzbin.info/aero/PLcfz9wmNxKqgciRucJOr8VdEQQT_cicOT

[@shivamnahata7451]

@@EngineeringEconomicsGuy thank you sir.

[@davidio1946]

​@@EngineeringEconomicsGuy Professor I'm confused on why you chose 5% and 6%? Like what's the logic behind those values? Is it because when we look at those percent tables with the corresponding n values we try to find the i* values that are closest to the number we solved for, in our case 5?

[@lauraparissi7846]

what if my y1 is a negative?

[@EngineeringEconomicsGuy]

If your y1 is a negative number, you've made a mistake! X1, x2, y1, and y2 should all be positive. Check the signs in your time-value-of-money equation. Hope this helps!

[@shaveenh.husien]

I used the equation and the same result I got it by calculator.

[@EngineeringEconomicsGuy]

OK - That method works!